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Title: The star-triangle relation, lens partition function, and hypergeometric sum/integrals
Authors: Gahramanov, Ilmar
Kels, Andrew P.
Keywords: Duality in Gauge Field Theories
Lattice Integrable Models
Supersymmetric gauge theory
Supersymmetry and Duality
Issue Date: 2017
Publisher: Springer
Citation: Journal of High Energy Physics
Abstract: The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens (S 3 b /Zr) partition functions, for certain three-dimensional N = 2 supersymmetric gauge theories.
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